Implicit–explicit numerical schemes for jump–diffusion processes |
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Authors: | Maya Briani Roberto Natalini Giovanni Russo |
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Affiliation: | (1) Istituto per le Applicazioni del Calcolo “Mauro Picone” – CNR, 00161 Rome, Italy, & LUISS Guido Carli, 00198 Rome, Italy;(2) Istituto per le Applicazioni del Calcolo “Mauro Picone” – CNR, 00161 Rome, Italy;(3) Dipartimento di Matematica Pura e Informatica, Università di Catania, 95129 Catania, Italy |
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Abstract: | Abstract
We study the numerical approximation of solutions for parabolic integro-differential equations (PIDE). Similar models arise
in option pricing, to generalize the Black–Scholes equation, when the processes which generate the underlying stock returns
may contain both a continuous part and jumps. Due to the non-local nature of the integral term, unconditionally stable implicit
difference schemes are not practically feasible. Here we propose using implicit-explicit (IMEX) Runge-Kutta methods for the
time integration to solve the integral term explicitly, giving higher-order accuracy schemes under weak stability time-step
restrictions. Numerical tests are presented to show the computational efficiency of the approximation.
Mathematics Subject Classification (1991): Primary: 65M12; Secondary: 35K55, 49L25 |
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Keywords: | |
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